This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A346376 #14 Jul 21 2021 09:33:23 %S A346376 28,204,604,1348,2580,4468,7204,11004,16108,22780,31308,42004,55204, %T A346376 71268,90580,113548,140604,172204,208828,250980,299188,354004,416004, %U A346376 485788,563980,651228,748204,855604,974148,1104580,1247668,1404204,1575004,1760908,1962780 %N A346376 a(n) = n^4 + 14*n^3 + 63*n^2 + 98*n + 28. %C A346376 The product of eight consecutive positive integers can always be expressed as the difference of two squares: x^2 - y^2. %C A346376 This sequence gives the x-values for each product. The y-values are A017113(n+4). %C A346376 a(n) is always divisible by 4. In addition, we have (a(n)+16)/4 belongs to A028387. %C A346376 Are 4 and 8 the unique values of k such that the product of k consecutive integers is always distant to upper square by a square? %H A346376 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A346376 a(n) = A239035(n)^2 - A017113(n+4)^2. %F A346376 a(n) = 4*(A028387(A046691(n+2)) - 4). %F A346376 G.f.: 4*(7 + 16*x - 34*x^2 + 22*x^3 - 5*x^4)/(1 - x)^5. - _Stefano Spezia_, Jul 14 2021 %Y A346376 Cf. A239035, A017113, A028387, A046691. %K A346376 nonn,easy %O A346376 0,1 %A A346376 _Lamine Ngom_, Jul 14 2021